Probing the quantum motion of a macroscopic mechanical oscillator with a radio-frequency superconducting qubit
Long-lived mechanical resonators like drums oscillating at MHz frequencies and operating in the quantum regime are a powerful platform for quantum technologies and tests of fundamental physics. Yet, quantum control of such systems remains challenging, owing to their low energy scale and the difficulty of achieving efficient coupling to other well-controlled quantum devices. Here, we demonstrate repeated coherent interactions between a 4 MHz suspended silicon nitride membrane and a resonant superconducting heavy-fluxonium qubit. The qubit is initialized at an effective temperature of $21~\mathrm{\mu K}$ and read out with 77% single-shot fidelity. During the $6~\mathrm{ms}$ lifetime of the membrane the two systems swap excitations more than 300 times. After each interaction, a state-selective qubit detection is performed, implementing a stroboscopic series of weak measurements that provide information about the mechanical state. The accumulated records reconstruct the position noise spectrum of the membrane, revealing both its thermal occupation $n_\mathrm{th}\approx47$ at $10~\mathrm{mK}$ and the qubit-induced back-action. By preparing the qubit either in its ground or excited state before each interaction, we observe an imbalance between the emission and absorption spectra, proportional to $n_\mathrm{th}$ and $n_\mathrm{th}+1$, respectively-a hallmark of the non-commutation of phonon creation and annihilation operators. Since the predicted Di\'osi-Penrose gravitational collapse time is comparable to the measured mechanical decoherence time, our architecture enters a regime where gravity-induced decoherence could be tested directly.